On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball
Let 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a hol...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/214762 |
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| Summary: | Let 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a holomorphic function f in 𝔹. We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0. |
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| ISSN: | 1085-3375 1687-0409 |